When we first meet Harry, he is an orphan being left on the doorsteps of his Uncle Vernon and Aunt Petunia's home. Harry was just a baby at this point so he doesn't remember the magical people who dropped him off. Later we meet up with Harry again on his eleventh birthday. This is a very vulnerable age for Harry and many readers. From what we can see Harry had to grow up very quickly. His Aunt and Uncle weren't very fond of him so they made him the live-in housekeeper. Learning how to cook, clean, and entertain himself with the very little that he had. Once he gets to school Harry learns that he is a much bigger person than he's been his whole life. He is a wizard, and not just any wizard, he's the boy who lived. Harry was raised to think that he wasn't good enough for anything. He thought he was a bastard child, and was only there to serve his family. When Harry finds out he is a wizard his response shows it all with the famous quote, "I can't be a wizard, I'm just Harry".
This makes Harry very relatable for many readers, especially at his age. When you turn 11 a lot of changes occur in your life. You've probably moved up from elementary school, to middle school or junior high. You're forced into new classes with new people that you didn't have with you in elementary school. As Harry grows into his new school so do many readers. Along the way you see the development of friendships that Harry makes. Which shows readers not to be nervous, everyone can find friends.
Harry's life wasn't easy either. Not everyone has the perfect home life that we want for them. Many actually harder lives than we can ever imagine. Seeing Harry overcome the obstacles that his neglectful family puts in his way is an inspiration for readers. If this boy can do it, why can't they? When readers are having a hard time at home they can escape to their rooms, bury their noses in the book and escape from the life they are living.